Nonlinear scattering of a Bose-Einstein condensate on a rectangular barrier

We consider the nonlinear scattering and transmission of an atom laser or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several physical features beyond the well-known picture from single-particle quantum mechanics. We find numerical evidence for a denumerably infinite string of bifurcations in the transmission resonances as a function of nonlinearity and chemical potential, when the potential barrier is wide compared to the wavelength of oscillations in the condensate. Near the bifurcations, we observe extended regions of near-perfect resonance, in which the barrier is effectively invisible to the BEC. Unlike in the linear case, it is mainly the barrier width, not the height, that controls the transmission behavior. We show that the potential barrier can be used to create and localize a dark soliton or dark-soliton train from a phononlike standing wave.